Perform the indicated operations and simplify.
-
A)r + s
B)r - s

Question

Perform the indicated operations and simplify.
-
A)r + s 
B)r - s

Quizplus · Accepted Answer

To add or subtract two numbers in this format, you need to flip the second number (change all 0's to 1's and 1's to 0's) and add 1. Then you can use binary subtraction. 
s = 11010100011101100001001011000100100100001000010110 
-r = 00101011100010011110110100111011011011110111101001 
Flipping and adding one gives: 11010100011101100001001011000100100100001000010111 
Using binary subtraction: 
s - r = 10101111101100110011011110111101100101101011001001 
This is the same as -(-10101111101100110011011110111101100101101011001001) in binary. Converting back to hex gives bbb7ccdfb526. 
So r - s = -bbb7ccdfb526 = 11ebbb8f_b96d_0921_bcf2_ff3a3aaaaa8a_TB8306_11, which is choice B. Subtracting s from r will cancel out the identical terms in the sum. Therefore, r - s is the simplified form.

Perform the Indicated Operations and Simplify